Most Korean markets are like that. Hell, most open street markets in other countries are like that. You see chickens, fish, ribs, everything just hanging open for you to see. What's the big deal? Hopefully you wash the meat before you cook it and if not, cooking the meat itself will kill anything that may be on there.
Dried fish are for eating. You'll see in most restaurants there that if you order a fresh plate with fish on it, that the fish is taken and killed right there, then served to you upon being cooked to your order. Usually the fish is still blinking and what-not while it's in front of you.
You'll get used to it. Not every country pumps their livestock full of hormones then shrink wraps them like the US.
